Final answer:
The sum of AB and BC must equal AC. Given the equation (x + 10) + (x + 14) = 22, the value of x cannot be negative as it would imply negative lengths, which is not possible. There may be a mistake in the values provided or the options for x.
Step-by-step explanation:
To solve for x when B is between A and C and given that AC = 22, BC = x + 14, and AB = x + 10, we can use the property that the sum of the lengths of AB and BC is equal to the length of AC.
So, we have the equation:
AB + BC = AC
(x + 10) + (x + 14) = 22
Combining like terms, we get:
2x + 24 = 22
Subtracting 24 from both sides gives us:
2x = -2
Dividing both sides by 2, we find:
x = -1
However, this value of x cannot be correct as it would result in negative lengths for AB and BC, which is not possible. It appears that there is a mistake in the given values or the options provided for the answer because with the given information, any value of x that satisfies AC = AB + BC must be positive. Please recheck the values provided.